Laptop with Windows 8 license and Win10 update: reinstall Win10?

I have a somewhat older laptop that was shipped with Windows 8.1 and "built in" the license key for it. I updated it when Windows 10 came out free of charge. Now I would like to format and reinstall it because I want to sell it. The question is, can I just put Windows 10 directly on it, or do I have to take Windows 8 and then update again?

No you can install Windows 10 immediately because the key is linked to your mainboard.

When upgrading to Win10 free of charge, the digital ID was saved on MS servers and is used to reactivate it when Win 10 is reinstalled on this computer without the need for a license key.

Very nice, saves me a lot of work.